A257792 Expansion of 1/(1-x-x^2-x^3-x^5+x^8-x^9).
1, 1, 2, 4, 7, 14, 26, 49, 92, 174, 328, 618, 1166, 2197, 4143, 7811, 14726, 27764, 52344, 98687, 186058, 350784, 661347, 1246865, 2350768, 4432000, 8355837, 15753609, 29700940, 55996428, 105572414, 199040101, 375258649, 707490872, 1333862213, 2514786376
Offset: 0
Examples
Example (1):Partial order of (n) into parts (1,2,3,5,9) where the adjacent order of 3's and 5's is unimportant. a(8)=92 These are (53=35)=1,(521)=6,(5111)=4,(332)=3,(3311)=6,(3221)=12,(32111)=20,(311111)=6,(2222)=1,(22211)=10,(221111)=15,(2111111)=7,(11111111)=1. Example (2):Partial order of (n) into parts (1,2,3,4,5,6) where the adjacent order of all odd numbers (i.e. 1,3,5) is unimportant. a(6)=26 These are (6),(51=15),(42),(24),(411),(141),(114),(33),(321),(123),(231=213),(312=132),(3111=1311=1131=1113),(222),(2211),(1122),(1221),(2112),(2121),(1212),(21111),(12111),(11211),(11121),(11112),(111111).
Links
- Index entries for related partition-counting sequences
- Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,1,0,0,-1,1).
Programs
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Magma
I:=[1,1,2,4,7,14,26,49,92]; [n le 9 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)+Self(n-5)-Self(n-8)+Self(n-9): n in [1..40]]; // Vincenzo Librandi, May 09 2015
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Mathematica
CoefficientList[Series[1/(1 - x - x^2 - x^3 - x^5 + x^8 - x^9), {x, 0, 80}], x] (* Vincenzo Librandi, May 09 2015 *) LinearRecurrence[{1,1,1,0,1,0,0,-1,1},{1,1,2,4,7,14,26,49,92},36] (* Ray Chandler, Jul 14 2015 *) -
Sage
m = 40; L.
= PowerSeriesRing(ZZ, m); f = 1/(1-x-x^2-x^3-x^5+x^8-x^9); print(f.coefficients()) # Bruno Berselli, May 12 2015
Formula
G.f.: 1/(1-x-x^2-x^3-x^5+x^8-x^9).
a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-5) - a(n-8) + a(n-9).
Extensions
More terms from Vincenzo Librandi, May 09 2015
Comments